[Table of Contents]

Plasma and Fusion Research

Volume 1, 038 (2006)

Regular Articles


Development of Computational Technique for Labeling Magnetic Flux-Surfaces
Masanori NUNAMI1), Ryutaro KANNO1), Shinsuke SATAKE1), Hisanori TAKAMARU2) and Takaya HAYASHI1,3)
1)
National Institute for Fusion Science
2)
Department of Computer Science, Chubu University
3)
Department of Fusion Science, Graduate University for Advanced Studies
(Received 3 March 2006 / Accepted 14 June 2006 / Published 8 August 2006)

Abstract

In recent Large Helical Device (LHD) experiments, radial profiles of ion temperature, electric field, etc. have been measured in the m/n = 1/1 magnetic island produced by island control coils, where m is the poloidal mode number and n the toroidal mode number. When the plasma transport in radial profiles is numerically analyzed, an average over a magnetic flux-surface in the island is a very useful concept to understand the transport. When averaging, a proper labeling of the flux-surfaces is necessary. In general, it is not easy to label the flux-surfaces in a magnetic field containing the island, compared with the case of a magnetic field configuration having nested flux-surfaces. In the present paper, we have developed a new computational technique to label the magnetic flux-surfaces. This technique uses an optimization algorithm called the simulated annealing method. The flux-surfaces are discerned by using two labels: one is classification of the magnetic field structure, i.e., core, island, ergodic, and outside regions, and the other depends on the value of the toroidal magnetic flux. We have applied this technique to an LHD configuration with the m/n = 1/1 island, and successfully discriminated of the magnetic field structure.


Keywords

Large Helical Device, magnetic island, flux-surface, Poincaré plots, annealing method

DOI: 10.1585/pfr.1.038


References

  • [1] S. Hamada, Nucl. Fusion 2, 23 (1962).
  • [2] A.H. Boozer, Phys. Fluids 23, 904 (1980).
  • [3] N. Nakajima, J. Todoroki and M. Okamoto, Kakuyugo Kenkyu 68, 395 (1992).
  • [4] H. Grad, Phys. Fluids 10, 137 (1967).
  • [5] T. Hayashi, Theory of Fusion Plasmas (Società Italiana di Fisica, Bologna, 1989) p.11.
  • [6] K. Harafuji, T. Hayashi and T. Sato, J. Comput. Phys. 81, 169 (1989).
  • [7] R. Kanno, T. Hayashi and M. Okamoto, Nucl. Fusion 45, 588 (2005).
  • [8] S.R. Hudson and R.L. Dewar, Phys. Lett. A 226, 85 (1997).
  • [9] R.L. Dewar, S.R. Hudson and P.F. Price, Phys. Lett. A 194, 49 (1998).
  • [10] J. Todoroki, J. Phys. Soc. Jpn. 58, 3979 (1989).
  • [11] J. Todoroki, J. Phys. Soc. Jpn. 63, 2168 (1994).
  • [12] M. Kurata and J. Todoroki, J. Plasma Fusion Res. SERIES 1, 491 (1998).
  • [13] K. Ida, N. Ohyabu, T. Morisaki et al., Phys. Rev. Lett. 88, 015002 (2002).
  • [14] K. Ida, S. Inagaki, N. Tamura et al., Nucl. Fusion 44, 290 (2004).
  • [15] G. Kuo-Petravic, A.H. Boozer, J.A. Rome and R.H. Fowler, J. Comput. Phys. 51, 261 (1983).
  • [16] J.A. Rome, J. Comput. Phys. 82, 348 (1989).
  • [17] P.H. Fowler, R.N. Morris, J.A. Rome and K. Hanatani, Nucl. Fusion 30, 997 (1990).
  • [18] H. Kikuchi, H. Ueno, M. Aizawa et al., Proceedings of the First International Toki Conference on Plasma Physics and Controlled Nuclear Fusion (National Institute for Fusion Science, Toki, 1990) p.183.
  • [19] S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, Science 220, 671 (1983).
  • [20] V.Cerný,J. Optim. Theory Appl. 45, 41 (1985).
  • [21] E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys (Ed), The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (John Wiley & Sons Ltd, Eastbourne, 1985).
  • [22] C.K. Koelbel, D.B. Loveman, R.S. Schreiber, G.L. Steele Jr. and M.E. Zosel, The High Performance Fortran Handbook (MIT Press, Cambridge Massachusetts, 1993).
  • [23] W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes in C (Cambridge University Press, New York, 1986).
  • [24] N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller, J. Chem. Phys. 21, 1087 (1953).
  • [25] J. Todoroki, Kakuyugo Kenkyu 57, 318 (1987) (in Japanese).
  • [26] J. Todoroki, Kakuyugo Kenkyu 63, 271 (1990) (in Japanese).
  • [27] J. Todoroki, Jpn. J. Appl. Phys. 43, 1209 (2004).
  • [28] W.X. Wang, N. Nakajima, M. Okamoto and S. Murakami, Plasma Phys. Control. Fusion 41, 1091 (1999).
  • [29] M. Okamoto, N. Nakajima, S. Satake and W.X. Wang, J. Plasma Fusion Res. 78, 1344 (2002).
  • [30] S. Satake, M. Okamoto, N. Nakajima, H. Sugama and M. Yokoyama, Plasma Fusion Res. 1, 002 (2006).
  • [31] P. Helander and D.J. Sigmar, Collisional Transport in Magnetized Plasmas (Cambridge University Press, Cambridge, 2002).
  • [32] R. Kanno, S. Jimbo, H. Takamaru and M. Okamoto, J. Plasma Fusion Res. SERIES 6, 527 (2004).
  • [33] S. Jimbo, R. Kanno, H. Takamaru and M. Okamoto, J. Plasma Fusion Res. 80, 649 (2004).
  • [34] S. Jimbo, R. Kanno, H. Takamaru, S. Satake and M. Okamoto, Nucl. Fusion 45, 1534 (2005).

This paper may be cited as follows:

Masanori NUNAMI, Ryutaro KANNO, Shinsuke SATAKE, Hisanori TAKAMARU and Takaya HAYASHI, Plasma Fusion Res. 1, 038 (2006).